For the first time in two years, the dollar was worth more than two marks in the international money markets yesterday, while gold plummeted to below $600 an ounce, closing at $564 in New York and at $582.50 in London. The last time that the dollar had topped the two-mark level in Frankfurt was in August 1978.

On Tuesday, West German Chancellor Helmut Schmidt had complained that the dollar, which has been rising steadily for the past several months, had become overvalued, and that the mark therefore had become too cheap. The dollar yesterday also hit a new high for the second day in a row against the lire, closing at 946.75 against 936.95 on Tuesday.

In London, the pound notched up to $2.34 from $2.3365 and to $2.3405 in New York.

European closing rates with late New York prices in parentheses:

Zurich, 1,8038 Swiss francs, up from 1.7895 (1.82); Paris, 4.63125 francs, up from 4.57625 (4.6350); Brussels, 32.135 Belgian francs, up from 31.9250 (32.27).

In Tokyo, the dollar eased to 209.25 Japanese yen from 209.30 and it inched up to 210 yen in New York.

Spokesman for U.S. Army headquarters in Europe hailed in the improved exchange rates against the German currency, noting that an increase of only one pfennig in the value of the dollar represents an annual saving of $7.5 million in the armed forces budget. For American servicemen, the higher value of their dollar pay meant an increase in their real income, in effect a welcome bonus just before Christmas.

Swiss money market experts attributed the rise of the dollar -- as well as the strength of the British pound -- to the record rise of interest rates in the United States and the high levels of interest rates in England.

In addition, a steady flow of American exports overseas, coupled with substantial earnings on investments, has counterbalanced the heavy costs for imported oil. Thus, the statistic that foreign exchange traders examine most closely -- the status of a nation's current account -- has worked in the United States' favor. At a time when both Germany and Japan are showing heavy current account deficits, the U.S. current account -- covering trade and services -- will be about in balance in 1980, and is expected to be in slight surplus in 1981.

The dollar's continued strength and the weakness in the gold markets had a common basis: the continued skyrocketing of American interest rates that saw the prime rate move back to the 20 percent level touched earlier this year. That level of interest rates -- which may not yet be the peak of the cycle -- is attracting investment funds from Europe, where rates are much lower.

In addition, gold suffered from a report that Soviet President Leonid Brezhnev, in a speech to the Indian parliament, had proposed a peach plan for the Persian Gulf and even left open the prospect that Soviet troops might be pulled out of Afghanistan.